Modelling and analysis of Parkinsonian gait

Abstract

Freezing of gait is a late-stage debilitating symptom of Parkinson’s disease (PD) characterised by a sudden involuntary stoppage of forward progression of gait. The present understanding of PD gait is limited, and there is a need to develop mathematical models explaining PD gait’s underlying mechanisms. A novel hybrid system model is proposed in this paper, in which a mechanical model is coupled with a neuronal model. The proposed hybrid system model has event-dependent feedback and demonstrates PD-relevant behaviours such as freezing, high variability and stable gait. The model’s robustness is studied by analysing relevant parameters such as gain in the event-dependent feedback and level of activation of the central pattern generator neurons. The effect of augmented feedback on the model is also studied to understand different FoG management methods, such as sensory and auditory cues. The model indicates the frequency-dependent behaviours in PD, which are in line with the STN stimulation and external cueing-related studies. The model allows one to estimate the parameters from the data and thereby personalise the cueing regimes for patients. The model can be of help in understanding the mechanism of FoG and developing measures to counter its severity.